Lessons from the 2003 Tokachi-oki, Japan, earthquake for prediction of long-period strong ground motions and sloshing damage to oil storage tanks

The 2003 Tokachi-oki earthquake (M _w 8.0) in northern Japan generated large-amplitude long-period (4–8 s) ground motions in the Yufutsu sedimentary basin, causing severe damage to seven large oil storage tanks with floating roof structures because of severe sloshing of oil. The 30,000–40,000-m³ tanks having suffered the severe damage such as fires and sinking of floating roofs experienced the sloshing with large amplitudes exceeding 3 m in which the fundamental mode was predominant. The second mode of sloshing was also excited in the 110,000-m³ tanks in which their floating roofs sank into oil, indicating that the higher modes of sloshing as well as the fundamental mode should be considered in damage prediction. The strong ground motion recordings demonstrated the earthquake dependency of predominant periods and the substantial spatial variation of the long-period shaking observed within the Yufutsu basin, meaning the necessity of source- and site-specific prediction of long-period strong ground motions. The two-dimensional numerical modeling suggested the importance of detailed structures of soft near-surface sediments as well as deep basin structure for accurate prediction of long-period strong ground motions in deep sedimentary basins.     

Nonlinear sloshing in a floating‐roofed oil storage tank under long‐period seismic ground motion

A hybrid analytical and FEM is proposed to investigate the nonlinear sloshing in a floating‐roofed oil storage tank under long‐period seismic ground motion. The tank is composed of a rigid cylindrical wall and a flat bottom, whereas the floating roof is treated as an elastic plate undergoing large deflection. The contained liquid is assumed to be inviscid and incompressible, and the flow is assumed to be irrotational. The method of analysis is based on representation of the liquid motion by superposing the analytical modes that satisfy the Laplace equation and the rigid wall and bottom boundary conditions. The FEM is then applied to solve the remaining kinematic and dynamic boundary conditions at the moving liquid surface coupled with the nonlinear equation of motion of the floating roof. This requires only the discretization of the liquid surface and the floating roof into finite elements, thus leading to a computationally efficient and accurate method compared with full numerical analysis. As numerical examples to illustrate the applicability of the proposed method, two oil storage tanks with single‐deck type floating roofs damaged during the 2003 Tokachioki earthquake are studied. It is shown that the nonlinear oscillation modes with the circumferential wave numbers 0, 2 and 3 caused by the finite liquid surface elevation as well as the membrane action due to large deflection of the deck produce excessively large stresses in the pontoon, which may cause the catastrophic failure of pontoon followed by the submergence of the roof. Copyright © 2012 John Wiley & Sons, Ltd.     

Dynamic buckling and seismic fragility of anchored steel tanks by the added mass method

Buckling plays a fundamental role in the design of steel tanks because of the small thicknesses of the walls of this class of structures. The first part of the paper presents a review of this phenomenon for liquid‐containing circular cylindrical steel tanks that are fully anchored at the base, considering the different buckling modes and especially the secondary buckling occurring in the top part of the tank. A case study based on a cylindrical tank is then introduced in order to investigate various aspects of dynamic buckling. The finite element model of the case study tank is set‐up using the added mass method for fluid modelling. The influence of pre‐stress states caused by hydrostatic pressure and self‐weight on the natural periods of the structure is first studied and it is found that this influence is very small as far as the global behaviour of the tanks is considered, while it is important for local, shell‐type, vibration modes. In the following, the efficiency and sufficiency of different ground motion intensity measures is analysed by means of cloud analysis with a set of 40 recorded accelerograms. In particular, the peak ground displacement has been found being the most efficient and sufficient intensity measure so far as the maximum relative displacement of the tank walls is concerned. Finally, incremental nonlinear time‐history analyses are performed considering the case study structure under recorded earthquake ground motions in order to identify the critical buckling loads and to derive fragility curves for the buckling limit state. Copyright © 2013 John Wiley & Sons, Ltd.     

Soil-structure interaction effects for laterally excited liquid storage tanks

A comprehensive study is made of the effects of soil-structure interaction on the response of liquid containing, upright, circular cylindrical tanks subjected to a horizontal component of ground shaking. A simple, physically motivated method of analysis is employed which elucidates the effects and relative importance of the principal actions involved. Both the impulsive and convective actions of the liquid are examined. The interrelationship of the tank responses to horizontal and rocking actions of the foundation is established, and the well known mechanical model for laterally excited, rigid tanks supported on a non-deformable medium is generalized to permit consideration of the effects of tank and ground flexibilities and base rocking. Critical responses are evaluated for harmonic and seismic excitations over wide ranges of tank proportions and soil stiffnesses, and the results are presented in a form convenient for use in practical applications. In addition to a precise method of analysis, an approximate, hand-computation method is presented with which the effects of the primary parameters may be evaluated readily. The soil-structure interaction effects in the latter approach are provided for by modifying the natural frequency and damping of the tank-liquid system and evaluating its response to the prescribed free-field ground motion considering the tank to be rigidly supported at the base. The requisite modifications may be determined from information presented herein. It is shown that soil-structure interaction may reduce significantly the impulsive components of response but that it has a negligible effect on the convective components.     

On the seismic behavior of cylindrical base-isolated liquid storage tanks excited by long-period ground motions

A common effective method to reduce the seismic response of liquid storage tanks is to isolate them at base using base-isolation systems. It has been observed that in many earthquakes, the foregoing systems significantly affect on the whole system response reduction. However, in exceptional cases of excitation by long-period shaking, the base-isolation systems could have adverse effects. Such earthquakes could cause tank damage due to excessive liquid sloshing. Therefore, the numerical seismic response of liquid storage tanks isolated by bilinear hysteretic bearing elements is investigated under long-period ground motions in this research. For this purpose, finite shell elements for the tank structure and boundary elements for the liquid region are employed. Subsequently, fluid–structure equations of motion are coupled with governing equation of base-isolation system, to represent the whole system behavior. The governing equations of motion of the whole system are solved by an iterative and step-by-step algorithm to evaluate the response of the whole system to the horizontal component of three ground motions. The variations of seismic shear forces, liquid sloshing heights, and tank wall radial displacements are plotted under various system parameters such as the tank geometry aspect ratio (height to radius), and the flexibility of the isolation system, to critically examine the effects of various system parameters on the effectiveness of the base-isolation systems against long-period ground motions. From these analyses, it may be concluded that with the installation of this type of base-isolation system in liquid tanks, the dynamic response of tanks during seismic ground motions can be considerably reduced. Moreover, in the special case of long-period ground motions, the seismic response of base-isolated tanks may be controlled by the isolation system only at particular conditions of slender and broad tanks. For the case of medium tanks, remarkable attentions would be required to be devoted to the design of base-isolation systems expected to experience long-period ground motions.     

浮放储罐三维地震反应有限元分析

针对立式储罐,考虑液固耦合效应、地基与储罐结构的相互作用,采用有限元分析方法,对储罐在三维地震荷载作用下动反应进行了数值分析。分析结果表明：储罐三维地震加速度反应较一维地震加速度反应增加、提离高度明显放大、储罐轴向应力增加、基底剪力与弯矩增大。     

地震作用下立式储液罐罐壁“象足”变形仿真分析

基于ANSYS软件建立了考虑液体晃动和罐底提离立式储液罐有限元模型,分别进行了水平地震和竖向地震作用下罐壁“象足”变形分析。分析表明:立式储液罐罐壁“象足”变形主要是由罐壁纵向压应力超过临界应力而产生的局部屈曲破坏,并非强度破坏。因罐底提离导致的罐底与基础反复撞击加大了作用在罐壁上的应力,使罐壁底部“象足”变形不断发展,最终导致罐壁撕裂。在完全相同地震加速度作用下,水平地震作用比竖向地震作用罐壁更早更容易进入屈曲状态,产生“象足”变形。     

地震作用下立式储液罐罐壁"象足"变形仿真分析

基于ANSYS软件建立了考虑液体晃动和罐底提离立式储液罐有限元模型,分别进行了水平地震和竖向地震作用下罐壁"象足"变形分析.分析表明:立式储液罐罐壁"象足"变形主要是由罐壁纵向压应力超过临界应力而产生的局部屈曲破坏,并非强度破坏.因罐底提离导致的罐底与基础反复撞击加大了作用在罐壁上的应力,使罐壁底部"象足"变形不断发展,最终导致罐壁撕裂.在完全相同地震加速度作用下,水平地震作用比竖向地震作用罐壁更早更容易进入屈曲状态,产生"象足"变形.     

Numerical investigation of stochastic response of an elevated water tank to random underground blast loading

This paper presents a stochastic finite element seismic response study of a water tank subjected to random underground blast-induced ground motion. Such tanks contain water and hazardous chemical substances, which implies significant risk to human life, serious environmental pollution, and considerable economic loss. The random blast-induced ground motion is represented by power spectral density function and applied to each support point of the three dimensional finite element model of the elevated water tank–fluid interaction system. A parametric study is conducted to estimate the effects of the blast-induced ground motion on the stochastic response of the elevated water tank system. Therefore, the analyses are carried out for different values of the charge weight and the distance from the charge centre. Additionally, in order to investigate the effect of the fluid on the stochastic response of the elevated water tank, three cases with different water levels are considered in the analyses. Finally, it is observed that underground blast loading considerably changes the stochastic behavior of the elevated water tank system.     

Dynamic stability characteristics of liquid-filled shells

A Galerkin Finite Element formulation for the dynamic stability analysis of liquid-filled shells is given in this paper. The coupling among the axial and circumferential modes is investigated. The dynamic stability characteristics of two liquid-filled storage tanks subjected to vertical, horizontal and rocking seismic excitations are presented. It is shown that a tall tank tends to buckle at distinct frequencies; and for cos θ-type ground excitation, cos 2θ, cos 3θ and cos 4θ are the dominant modes of failure. On the other hand, in a broad tank, buckling regions overlap each other. In particular, for cos θ-type ground excitation, the dominant buckling modes are cos 6θ to cos 9θ, and also cos 12θ to cos 14θ.     

A seismological overview of long-period ground motion

Long-period ground motion has become an increasingly important consideration because of the recent rapid increase in the number of large-scale structures, such as high-rise buildings and oil storage tanks. Large subduction-zone earthquakes and moderate to large crustal earthquakes can generate far-source long-period ground motions in distant sedimentary basins with the help of path effects. Near-fault long-period ground motions are generated, for the most part, by the source effects of forward rupture directivity. Far-source long-period ground motions consist primarily of surface waves with longer durations than near-fault long-period ground motions. They were first recognized in the seismograms of the 1968 Tokachi-oki and 1966 Parkfield earthquakes, and their identification has been applied to the 1964 Niigata earthquake and earlier earthquakes. Even if there is no seismogram, we can identify far-source long-period ground motions through the investigation of tank damage by liquid sloshing.     

Simulation of accelerograms from simplified deterministic approach for the 23rd October 2004 Niigata-ken Chuetsu,Japan earthquake

A simple hybrid approach for the simulation of strong ground motion is presented in this paper. This approach is based on the deterministic modelling of rupture plane initially started by Midorikawa, Tectonophysics 218:287–295, (1993) and further modified by Joshi, Pure Appl Geophys (PAGEOPH) 8:161, (2004). In this technique, the finite rupture plane of the target event is divided into several subfaults, which satisfy scaling relationship. In this paper, simulation of strong ground motion due to a rupture buried in a earth medium consisting of several layers of different velocities and thicknesses is made by considering (1) transmission of energy at each layer; (2) frequency filtering properties of medium and earthquake source; (3) correction factor for slip of large and small magnitude earthquakes and (4) site amplification ratio at various stations. To test the efficacy of the developed technique, strong motion records were simulated at different stations that have recorded the 2004 Niigata-ken Chuetsu, Japan earthquake (M _s 7.0). Comparison is made between the simulated and observed velocity and acceleration records and their response spectra. Distribution of peak ground acceleration, velocity and displacement surrounding the rupture plane is prepared from simulated and observed records and are compared with each other. The comparison of synthetic with the observed records over wide range of frequencies shows that the present technique is effective to predict various strong motion parameters from simple deterministic model which is based on simple regression relations and modelling parameters.     

水平地震激励下储罐液体晃动与提离分析

在考虑地基与储罐相互作用的情况下,采用有限元法对储罐在水平地震荷载作用下的液面晃动及储罐提离反应进行了分析。结果表明:罐内液体的晃动是长周期运动,其周期受地震动影响。无论是小体积罐还是大体积罐,在一定的地震烈度下均可以发生提离,而且储罐发生提离的时刻大多数是在地震动的峰值过后的一段时间内。大体积的储罐的提离明显小于小体积的罐。底板提离区域为月牙形。     

大型储液罐摩擦摆基底隔震控制分析

针对弹性钢制圆柱储液罐,基于Haroun-Housner模型,将连续流体质量等效为3种集中质量,分别为:对流质量、脉冲质量和刚性质量,与这些集中质量连接的相应刚度取值依赖于储罐壁和流体质量.在水平地震激励下,在储罐底部加摩擦单摆支座,给出了简化的液体 - 储罐-隔震支座的力学分析模型,建立了摩擦摆支座基底隔震体系的振动控制方程,并利用Newmark逐步积分法对控制方程进行了数值求解,研究了摩擦摆支座基底隔震的储液罐地震反应,验证了FPB隔震的有效性.     

Seismic fragility of base-isolated water storage tanks under non-stationary earthquakes

Seismic fragility curves for fixed-base and base-isolated liquid storage tanks are developed under non-stationary earthquakes, and their seismic performance are compared. The correlation between different earthquake intensity measure (IM) parameters and peak response quantities of the base-isolated liquid storage tanks are investigated. The failure criteria are chosen based on (1) the elastic buckling strength of the tank wall, which is defined in terms of critical base shear and critical overturning moment, and (2) in terms of the critical isolation displacement. The uncertainty involved is considered in the earthquake characteristics. Non-stationary earthquake ground motions are generated using Monte Carlo (MC) simulation. Influence of the isolator characteristic parameters and modeling approaches on the seismic fragility of the base-isolated liquid storage tanks is also investigated. Peak ground acceleration is found to be the well correlated IM parameter with the peak response quantities of the base-isolated liquid storage tanks. Substantial decrease in the seismic fragility of the base-isolated liquid storage tanks is observed as compared to the fixed-base tanks. Significant influence of the isolator characteristic parameters on the seismic fragility of the base-isolated liquid storage tanks are reported in the present study.     

地下储液罐抗爆炸地冲击作用的流固耦合有限元分析

储液罐的抗震性能虽然得到了较为深入的研究,但对其抗爆炸产生的地冲击作用的研究还十分罕见。本文通过建立流固耦合的数值分析模型,研究爆炸地冲击作用下地下立式储液罐的动力特性,包括储液晃动波高、罐壁的应力和应变、底板的提离和浮放储液罐的“象足”变形产生原因及破坏机理等。研究结果表明,储液罐在爆炸地冲击荷载和地震荷载作用下的动力响应有明显区别,地震荷载作用下的储液罐抗震验算方法不适用于爆炸地冲击荷载。     

液压阻尼系统控制浮放立式储罐提离失稳

立式圆柱储罐在油田、石油化工等企业用途广泛，多用作存贮易燃、易爆介质，一旦遭遇震害，后果将十分严重。本文针对浮放立式储罐地震响应的提离失稳问题，采用液压阻尼系统（HDS）用以控制储罐的提离反应，建立了安装HDS储罐的力学分析模型并进行了数值计算，对安装HDS后储罐的提离反应进行了分析。仿真计算结果表明：HDS可以有效地减小提离应力，从而地震烈度可以降低1度进行储罐的提离设计。     

Non‐stationary seismic response of tanks with soil interaction by wavelets

A wavelet‐based random vibration theory has been developed for the non‐stationary seismic response of liquid storage tanks including soil interaction. The ground motion process has been characterized via estimates of statistical functionals of wavelet coefficients obtained from a single time history of ground accelerations. The tank–liquid–soil system has been modelled as a two‐degree‐of‐freedom (2‐DOF) system. The wavelet domain equations have been formulated and the wavelet coefficients of the required response state are obtained by solving two linear simultaneous algebraic equations. The explicit expression for the instantaneous power spectral density function (PSDF) in terms of the functionals of the input wavelet coefficients has been obtained. The moments of this PSDF are used to estimate the expected pseudo‐spectral acceleration (PSA) response of the tank. Parametric variations are carried out to study the effects of tank height, foundation natural frequency, shear wave velocity of soil and ratio of the mass of tank (including liquid) to the mass of foundation on the PSA responses of tanks. Copyright © 2001 John Wiley & Sons, Ltd.     

Fluid–structure interaction analysis of 3-D rectangular tanks by a variationally coupled BEM–FEM and comparison with test results

A variationally coupled BEM–FEM is developed which can be used to analyse dynamic response, including free-surface sloshing motion, of 3-D rectangular liquid storage tanks subjected to horizontal ground excitation. The tank structure is modelled by the finite element method and the fluid region by the indirect boundary element method. By minimizing a single Lagrange function defined for the entire system, the governing equation with symmetric coefficient matrices is obtained. To verify the newly developed method, the analysis results are compared with the shaking-table test data of a 3-D rectangular tank model and with the solutions by the direct BEM–FEM. Analytical studies are conducted on the dynamic behaviour of 3-D rectangular tanks using the method developed. In particular, the characteristics of the sloshing response, the effect of the rigidity of adjacent walls on the dynamic response of the tanks and the orthogonal effects are investigated. © 1998 John Wiley & Sons, Ltd.     

The effect of seismic uplift on the shell stresses of liquid‐storage tanks

Previous theoretical studies have shown that tank uplift, that is, separation of the tank base from the foundation, generally reduces the base shear and the base moment. However, there is a paucity of experimental investigations concerning the effect of uplift on the tank wall stresses, which is the principal parameter that controls the seismic design of liquid‐storage tanks. This paper reports a series of shake table experiments on a polyvinyl chloride model tank containing water. A comparison of the seismic behaviour of the tank with and without anchorage is described. Stochastically generated ground motions, based on a Japanese design spectrum, and three tank aspect ratios (liquid‐height/radius) are considered. Measurements were made of the stresses at the outer shell of the tank, the tank wall acceleration and the horizontal displacement at the top of the tank. While the top displacement and the tank shell acceleration increased when uplift was allowed, axial compressive stresses decreased by between 35% and 64% with tank uplift. The effect of uplift on the hoop stresses was variable depending on the aspect ratio. A comparison of experimental values with a numerical model is provided. Copyright © 2015 John Wiley & Sons, Ltd.